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On the nonlinear (k,Ψ)-Hilfer fractional differential equations

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  • Kucche, Kishor D.
  • Mali, Ashwini D.

Abstract

In the current paper, we present the most generalized variant of the Hilfer derivative so-called (k,Ψ)-Hilfer fractional derivative operator. The (k,Ψ)-Riemann-Liouville and (k,Ψ)-Caputo fractional derivatives are obtained as a special case of (k,Ψ)-Hilfer fractional derivative. We demonstrate a few properties of (k,Ψ)-Riemann-Liouville fractional integral and derivative that expected to build up the calculus of (k,Ψ)-Hilfer fractional derivative operator. We present some significant outcomes about (k,Ψ)-Hilfer fractional derivative operator that require to derive the equivalent fractional integral equation to nonlinear (k,Ψ)-Hilfer fractional differential equation. We prove the existence and uniqueness for the solution of nonlinear (k,Ψ)-Hilfer fractional differential equation. In the conclusion section, we list the various k-fractional derivatives that are specific cases of (k,Ψ)-Hilfer fractional derivative.

Suggested Citation

  • Kucche, Kishor D. & Mali, Ashwini D., 2021. "On the nonlinear (k,Ψ)-Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006895
    DOI: 10.1016/j.chaos.2021.111335
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    Cited by:

    1. Sotiris K. Ntouyas & Bashir Ahmad & Jessada Tariboon & Mohammad S. Alhodaly, 2022. "Nonlocal Integro-Multi-Point ( k , ψ )-Hilfer Type Fractional Boundary Value Problems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    2. Marisa Kaewsuwan & Rachanee Phuwapathanapun & Weerawat Sudsutad & Jehad Alzabut & Chatthai Thaiprayoon & Jutarat Kongson, 2022. "Nonlocal Impulsive Fractional Integral Boundary Value Problem for ( ρ k , ϕ k )-Hilfer Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(20), pages 1-40, October.
    3. Sotiris K. Ntouyas & Bashir Ahmad & Jessada Tariboon, 2022. "( k , ψ )-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions," Mathematics, MDPI, vol. 10(15), pages 1-20, July.

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